Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Spectroscopic and electrochemical properties of iron(II) complexes of polydentate Schiff bases containing pyrazine, pyridine and imidazole groups

We report the synthesis and spectroscopic/electrochemical properties of iron(II) complexes of polydentate Schiff bases generated from 2-acetylpyridine and 1,3-diaminopropane, acetylpyrazine and 1,3-diaminopropane, and from 2-acetylpyridine and L-histidine. The complexes exhibit bis(diimine)iron(II) chromophores in association with pyrazine, pyridine or imidazole groups displaying contrasting pi-acceptor properties. In spite of their open geometry, their properties are much closer to those of macrocyclic tetraimineiron(II) complexes. An electrochemical/spectroscopic correlation between E degrees(Fe(III/II)) and the energies of the lowest MLCT band has been observed, reflecting the stabilization of the HOMO levels as a consequence of the increasing backbonding effects in the series of compounds. Mossbauer data have also confirmed the similarities in their electronic structure, as deduced from the spectroscopic and theoretical data. (C) 2008 Elsevier B.V. All rights reserved.

Synthesis, spectroscopic characterization and X-ray structures of five-coordinate diorganotin(IV) complexes containing 5-hydroxypyrazoline derivatives as ligands

Four new diorganotin(IV) complexes have been prepared from R(2)SnCl(2) (R = Me, Ph) with the ligands 5-hydroxy-3-metyl-5-phenyl-1-(S-benzildithiocarbazate)-pyrazoline (H(2)L(1)) and 5-hydroxy-3-methyl-5-phenyl-1-(2-thiophenecarboxylic)-pyrazoline (H(2)L(2)). The complexes were characterized by elemental analysis, IR. (1)H (13)C, (119)Sn NMR and Mossbauer spectroscopes The complexes [Me(2)SnL(1)], [Ph(2)SnL(1)] and [Me(2)SnL(2)] were also studied by single crystal X-ray diffraction and the results showed that the Sn(IV) central atom of the complexes adopts a distorted trigonal bipyramidal (TBP) geometry with the N atom of the ONX-tridentate (X = O and S) ligand and two organic groups occupying equatorial sites. The C-Sn-C angles for [Me(2)Sn(L(1))] and [Ph(2)Sn(L(1))] were calculated using a correlation between (119)Sn Mossbauer and X-ray crystallographic data based on the point-charge model Theoretical calculations were performed with the B3LYP density functional employing 3-21G(*) and DZVP all electron basis sets showing good agreement with experimental findings General and Sn(IV) specific IR harmonic frequency scale factors for both basis sets were obtained from comparison with selected experimental frequencies (C) 2010 Elsevier B V All rights reserved

Análise dinâmica de vigas assimétricas em curva com parede fina e aberta submetidas a ação de carga móveis

Fundamentalmente, o presente trabalho faz uma análise elástica linear de pontes ou vigas curvas assimétricas de seção transversal aberta e de parede fina, com propriedades físicas, geométricas e raio de curvatura constantes ao longo do eixo baricêntrico. Para tanto, utilizaram-se as equações diferenciais de VLASOV considerando o acoplamento entre as deformações nas direções vertical, transversal, axial de torcão nal. Na solução do sistema de quatro equações com derivadas parciais foi utilizado um apropriado método numérico de integração (Diferenças Finitas Centrais). A análise divide-se, basicamente, em dois tipos: análise DINÂMICA e ESTATICA. Ambas são utilizadas também na determinação do coeficiente de impacto (C.M.D.). A primeira refere-se tanto na determinação das características dinâmicas básicas (frequências naturais e respectivos modos de vibração), como também na determinação da resposta dinâmica da viga, em tensões e deformações, para cargas móveis arbitrárias. Vigas com qualquer combinação das condições de contorno, incluindo bordos rotulados e engastados nas três direções de flexão e na torção, são consideradas. 0s resultados da análise teórica, obtidos pela aplicação de programas computacionais implementados em microcomputador (análise estática) e no computador B-6700 (análise dinâmica), são comparados tanto com os da bibliografia técnica como também com resultados experimentais, apresentando boa correlação.

Modelagem e simulação de um sistema de bombeio mecânico em poços direcionais utilizando parâmetros concentrados

This work aims presenting the development of a model and computer simulation of a sucker rod pumping system. This system take into account the well geometry, the flow through the tubing, the dynamic behavior of the rod string and the use of a induction motor model. The rod string were modeled using concentrated parameters, allowing the use of ordinary differential equations systems to simulate it s behavior

As geometrias urbana e isoperimétrica: uma alternativa de uso em sala de aula

The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Exotic dark spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estruturas tectônicas cenozóicas na porção leste da Bacia Potiguar - RN

This thesis encompasses the integration of geological, geophysical, and seismological data in the east part of the Potiguar basin, northeastern Brazil. The northeastern region is located in South American passive margin, which exhibits important areas that present neotectonic activity. The definition of the chronology of events, geometry of structures generated by these events, and definition of which structures have been reactivated is a necessary task in the region. The aims of this thesis are the following: (1) to identify the geometry and kinematics of neotectonic faults in the east part of the Potiguar basin; (2) to date the tectonic events related to these structures and related them to paleoseismicity in the region; (3) to present evolutional models that could explain evolution of Neogene structures; (4) and to investigate the origin of the reactivation process, mainly the type of related structure associated with faulting. The main type of data used comprised structural field data, well and resistivity data, remote sensing imagery, chronology of sediments, morphotectonic analysis, x-ray analysis, seismological and aeromagnetic data. Paleostress analysis indicates that at least two tectonic stress fields occurred in the study area: NSoriented compression and EW-oriented extension from the late Campanian to the early Miocene and EW-oriented compression and NS-oriented extension from the early Miocene to the Holocene. These stress fields reactivated NE-SW- and NW-SE-trending faults. Both set of faults exhibit right-lateral strike-slip kinematics, associated with a minor normal component. It was possible to determine the en echelon geometry of the Samambaia fault, which is ~63 km long, 13 km deep, presents NE-SW trend and strong dip to NW. Sedimentfilled faults in granite rocks yielded Optically Stimulated Luminescence (OSL) and Single-Aliquot Regeneration (SAR) ages at 8.000 - 9.000, 11.000 - 15.000, 16.000 - 24.000, 37.000 - 45.500, 53.609 - 67.959 e 83.000 - 84.000 yr BP. The analysis of the ductile fabric in the João Câmara area indicate that the regional foliation is NE-SW-oriented (032o - 042o), which coincides with the orientation of the epicenters and Si-rich veins. The collective evidence points to reactivation of preexisting structures. Paleoseismological data suggest paleoseismic activity much higher than the one indicated by the short historical and instrumental record

Differential pulse voltammetric determination of nitrite with gold ultramicroelectrode

The application of disk shaped gold ultramicroelectrode for nitrite determination with and without addition of supporting electrolyte was studied using the differential pulse voltammetric method. The well-defined peak for nitrite oxidation near 0.8V (vs. Ag/AgCl reference electrode) was used to obtain analytical plots in the concentration range from 0.1 to 0.6 mmol L-1 and from 10.0 to 50.0 mu mol.L-1. The calculated detection limit was 0.65 mu mol.L-1 in purified water, in the absence of supporting electrolyte, with relative standard deviation of 1.36% (n=6) for analyzing 10.0 mu mol L-1 nitrite solutions, and accuracy of 100.9 %, based on recovery studies. The application of this analytical method to mineral and river water samples of natural pH also showed improved sensitivity when compared with the linear sweep voltammetric method previously reported.

A solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica for differential pulse adsorptive stripping analysis of nickel in ethanol fuel

A solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica (SiAt-SPCPE) was applied to Ni2+ determination in commercial ethanol fuel samples. The proposed method comprised four steps: (1) Ni2+ preconcentration at open circuit potential directly in the ethanol fuel sample, (2) transference of the electrode to an electrochemical cell containing DMG, (3) differential pulse voltammogram registering and (4) surface regeneration by polishing the electrode. The proposed method combines the high Ni2+ adsorption capacity presented by 2-aminothiazole organofunctionalized silica with the electrochemical properties of the Ni(DMG)2 complex, whose electrochemical reduction provides the analytical signal.All experimental parameters involved in the proposed method were optimized. Using a preconcentration time of 20 min, it was obtained a linear range from 7.5 x 10(-9) to 1.0 x 10(-6) mol L-1 with detection limit of 2.0 x 10(-9) mol L-1. Recovery values between 96.5 and 102.4% were obtained for commercial samples spiked with 1.0 mu mol L-1 Ni2+ and the developed electrode was totally stable in ethanolic solutions. The contents of Ni2+ found in the commercial samples using the proposed method were compared to those obtained by graphite furnace atomic absorption spectroscopy by using the F- and t-test. Neither the F- nor t-values exceeded the critical values at 95% confidence level, confirming that there are not statistical differences between the results obtained by both methods. These results indicate that the developed electrode can be successfully employed to reliable Ni2+ determination in commercial ethanol fuel samples without any sample pretreatment or dilution step. (c) 2006 Elsevier B.V. All rights reserved.

Copper determination in ethanol fuel by differential pulse anodic stripping voltammetry at a solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica

Solid paraffin-based carbon paste electrodes modified with 2-aminothiazole organofunctionalized silica have been applied to the anodic stripping determination of copper ions in ethanol fuel samples without any sample treatment. The proposed method comprised four steps: (1) copper ions preconcentration at open circuit potential directly in the ethanol fuel sample; (2) exchange of the solution and immediate cathodic reduction of the absorbate at controlled potential; (3) differential pulse anodic stripping voltammetry; (4) electrochemical surface regeneration by applying a positive potential in acid media. Factors affecting the preconcentration, reduction and stripping steps were investigated and the optimum conditions were employed to develop the analytical procedure. Using a preconcentration time of 20 min and reduction time of 120 s at -0.3 V versus Ag/AgCl(sat) a linear range from 7.5 x 10(-8) to 2.5 x 10(-6) mol L(-1) with detection limit of 3.1 x 10(-8) mol L(-1) was obtained. Interference studies have shown a decrease in the interference effect according to the sequence: Ni > Zn > Cd > Pb > Fe. However, the interference effects of these ions have not forbidden the application of the proposed method. Recovery values between 98.8 and 102.3% were obtained for synthetic samples spiked with known amounts of Cu(2+) and interfering metallic ions. The developed electrode was successfully applied to the determination of Cu(2+) in commercial ethanol fuel samples. The results were compared to those obtained by flame atomic absorption spectroscopy by using the F-test and t-test. Neither F-value nor t-value have exceeded the critical values at 95% confidence level, confirming that there are no significant differences between the results obtained by both methods. (c) 2006 Elsevier B.V. All rights reserved.

Differential responses between mature and young leaves of sunflower plants to oxidative stress caused by water deficit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)